I would second Eleusis as a great game for training logical thinking. If you haven't played, at it's core, its basically the 2-4-6 game, with one of the players allowed to make up more complex rules. I've played several times with my friends, and you would be amazed at how difficult it is to tease out even some of the simpler rules. For instance, I once played a game, where a player went through almost 2 decks of cards before realizing the rule was "Alternate Red/Black".